This formula works with extract given in weight percentages and degree Plato. Since, at least in the wort and beer gravities that most brewers work with, there is an almost linear relationship between (specific gravity - 1) and extract percentages. This formula can be changed to:

Contents

Brewing process and wort composition

To understand the different forms of attenuation we need to take a look at the extract composition first. During mashing, the majority of the grist is converted into water soluble compounds and then to beer. This is shown in Figure 1.

Figure 1 - from grist to beer

The conditions during the mashing process as well as the grains will determine the exact ratio between the various compopunds (sugars, detxtrines, proteins and others). Once the conversion is complete, the mash is lautered. During this process not all of the dissolved extract is extracted. The perentage of the total dissolved extract and the extract that actually ends up in the boil kettle is called brew house efficiency.

During the boil only minor changes happen to the wort composition. The denaturization of the enzymes finally fixes the ratio between fermentable and unfermentable extract. Coagulation of proteines change the amount and composition of proteins in the wort. Hops will add additional compounds. But these are of little interest for the discussion of attenuation.

When during the wort fermentation, the fermentable sugars are converted into almost equal parts of CO2 and ethanol as well as much smaller amounts of other compounds (esters, higher alcohols). The yeast will also absorb most of the simple proteins. But not all of the fermentable sugars will have been fermented at the time the beer is comsumed. The amount of fermentable sugars left in the beer has an affect on the beer character and different styles of beer oftentimes have different amounts of fermentable sugars left.

Apparent vs. real extract

Hydometers are calibrtated for measuring the sugar (extract) content of a water soulution. This is true for wort. But when they are used to measure the extract of beer, which contains ethanol, the reading will be skewed by the lower specific gravity of the ethanol. As a result the hydrometer shows a lower extract content than the actual beer has. This measured extract value is called apparent extract (as opposed to the real extract that is measured when there is no alcohol in the solution) and is commonly used when refering to the extract (or specific gravity) of beer. Like the real extract it can be expressed as weight percent, degree plato or specific gravity. To determine the real extract one can boil-off the alcohol and replace it with distilled water before using a hydrometer. If the original extract is known the following formula [Realbeer] can be used to calculate the real extract from the apparent extract:

real extract = 0.1808 * original extract + 0.8192 * apparant extract

Apparent vs. real attenuation

When the apparent extract of the beer is used to calculate its attenuation it is called apparent attenuation. The use of the real extract will give the real attenuation. When brewers speak of just attenuation they are most likely to mean apparent attenuation since it can easily be calculated from the hydrometer readings.

Limit of attenuation

The Limit of attenuation is the sum of all the sugars that the yeast is able to ferment expressed as a percentage of the total extract content. Since ale yeasts (saccharomyces cerevisiae) can only ferment maltotriose to a third and lager yeasts (saccharomyces uvarum) can ferment that wort sugar completely, lager yeasts will show a slighly higher limit of attenuation for the same wort.

Other than this the limit of attenuation of a given wort does not depend on the yeast strain. It is soley set by the mashing process. All yeasts are able to ferment all the fermentable sugars (save for the lager - ale difference mentioned above) in a given wort. This fact is taken advantage of in a [forced ferment test]. The forced ferment test uses a sample of wort and pitches it with a large amount of yest. To ensure complete fermentation this sample is kept warm and the yeast is roused regularily (shaking or stir plate). Once the fermentation is complete the apparent extract is measured and the limit of attenuation for that wort can be calculated.

Yeast strain differences in attenuation

If there are no limit of attenuation differences between the different yeast strains, why are there more and less attenuative yeast strains available? Though yeast strains are able to ferment all the sugars in the beer, they usually don't get to. In contrast to a fast ferment test beer is fermented at lower temperatures, with smaller pitching rates and without constant rousing. Because of that the yeast will not get a chance to ferment all sugars in the wort. flocculation will cause it to drop to the bottom or collect on the surface where it doesn't have as much wort contact anymore. Because of nutrient depletion and or high alcohol levels cells die before they get a chance to ferment every last sugar in the wort. The result are left over fermentable sugars that play an imporant role in the character of the beer. The closer a beer's attenuation is to its limit of attenuation the drier and less sweet it will tase. When looking at the attenuation ranges given for commercial yeast you will notice that the less flocculating a yeast is, the more attenuative it will be. This makes sense as the less fluculating teasts will ramain in contact with the wort for a longer time.

[Narziss] lists ranges for attenuation (removal of the yeast) to limit of attenuation differences for different german beer types:

Helles : 2 - 4%

Export : 0.5 - 2 %

Pilsner : 0.5 - 4 %

Bock, Dunkel : up to 6 %

Example: A Helles with a target attenuation difference of 3% should be brewed. The wort as an original extract of 12.0 *P abd a limit of attenuation of 2.0 *P. The resulting limit of attenuation is 100% * (12-2.0)/12 = 83%. The target attenuation at bottling time is 83% - 3% = 80%. This attenuation is reached when the beer has an apparent extract of 12 - 12 * 80%/100% = 2.4 *P. But hitting this number exactly is difficult. One way would be to regularily measure the extact of the lagering beer and pull it off the yeast into a serving keg when the desired final extract is reached.

Even if a brewer doesn't go to this extend of control over the beer, performing a forced ferment test and comparing the limit of attenuation to the current attenuation can be helpful in understanding the taste character of a beer.

attenuation listed for yeast strains

As mentioned above, choice of yeast strain also affects the actual attenuation of the beer. As a guideline yeast vendors like Wyeast and White Labs list attenuations with their yeasts. But since the yeast strain is only one factor in attenuation (other important factors are mashing and yeast health) these attenuation values are useful to compare yeasts with each other and cannot be used to predict the final extract (or final gravity) of the beer. This can only be done with a fast ferment test.